Is it Easier to Transition from Math to Physics or Vice Versa?

[Bohr_Wars]

It seems to me that it is easier to start out as a mathematician and become a physicist than the other way round. There are plenty of math specialists branching out into physics, cosmology, etc. How many physics specialists go the other way? Physicists are always seeking mathematicians to help them out.

Is this a mistaken view? I feel inclined to focus on math, leaving the door open to a physics career later on.

 

[arunma]

Well, I don't have any statistics on this. But as my dad says, "physicists are always good at math, but not all mathematicians are good at physics." I've found this to be a generally accurate guideline. I've never met a physics major who had trouble in his math courses. But some of the brightest math students out there sometimes have trouble in physics. I know one math major who was essentially a child prodigy. Just to give you some perspective, when he and I took differential geometry together, he was only a senior in high school. The kid could basically do math in his sleep. So it really surprised me when he mentioned that he was struggling in physics 2.

From what I've seen, the mathematicians who go into physics usually stay on the periphery, working on theoretical or computational problems. Mathematicians are really good at computer modelling, as well as...well, math. So I suppose that things like string theory, theoretical particle physics, general relativity, etc., come easy to them. But I doubt you'd find many mathematicians designing the electronics for high energy detectors, or working on other such experimental problems.

I could certainly see a physicist going into math. In fact I happen to have a math degree, so I think I could work fairly competently as a professional mathematician. But I've got to ask: why would you want to do this? Professional mathematicians work on boring problems, like proving that some theorem about minimal surfaces can stand even if the fourteenth lemma of corollory X isn't assumed. Maybe it's just me, but compared to physics, math just seems a little dull.

 

[Beeza]

Well, I don't have any statistics on this. But as my dad says, "physicists are always good at math, but not all mathematicians are good at physics." I've found this to be a generally accurate guideline. I've never met a physics major who had trouble in his math courses. But some of the brightest math students out there sometimes have trouble in physics. I know one math major who was essentially a child prodigy. Just to give you some perspective, when he and I took differential geometry together, he was only a senior in high school. The kid could basically do math in his sleep. So it really surprised me when he mentioned that he was struggling in physics 2.

From what I've seen, the mathematicians who go into physics usually stay on the periphery, working on theoretical or computational problems. Mathematicians are really good at computer modelling, as well as...well, math. So I suppose that things like string theory, theoretical particle physics, general relativity, etc., come easy to them. But I doubt you'd find many mathematicians designing the electronics for high energy detectors, or working on other such experimental problems.

I could certainly see a physicist going into math. In fact I happen to have a math degree, so I think I could work fairly competently as a professional mathematician. But I've got to ask: why would you want to do this? Professional mathematicians work on boring problems, like proving that some theorem about minimal surfaces can stand even if the fourteenth lemma of corollory X isn't assumed. Maybe it's just me, but compared to physics, math just seems a little dull.

You do realize you've probably just offended several members of this board right?

 

[cristo]

You do realize you've probably just offended several members of this board right?

How can a personal opinion offend anyone?

 

[pivoxa15]

Well, I don't have any statistics on this. But as my dad says, "physicists are always good at math, but not all mathematicians are good at physics." I've found this to be a generally accurate guideline. I've never met a physics major who had trouble in his math courses. But some of the brightest math students out there sometimes have trouble in physics. I know one math major who was essentially a child prodigy. Just to give you some perspective, when he and I took differential geometry together, he was only a senior in high school. The kid could basically do math in his sleep. So it really surprised me when he mentioned that he was struggling in physics 2.

From what I've seen, the mathematicians who go into physics usually stay on the periphery, working on theoretical or computational problems. Mathematicians are really good at computer modelling, as well as...well, math. So I suppose that things like string theory, theoretical particle physics, general relativity, etc., come easy to them. But I doubt you'd find many mathematicians designing the electronics for high energy detectors, or working on other such experimental problems.

I could certainly see a physicist going into math. In fact I happen to have a math degree, so I think I could work fairly competently as a professional mathematician. But I've got to ask: why would you want to do this? Professional mathematicians work on boring problems, like proving that some theorem about minimal surfaces can stand even if the fourteenth lemma of corollory X isn't assumed. Maybe it's just me, but compared to physics, math just seems a little dull.

I seem to have the opposite experience whereby the physics students seem to struggle with the maths when it gets a little complex. Basically the mathematically able students are better at physics. To compare someone who has done a subject and hasn't about knowledge in the subject is unfair.

I can't see a physicist going into math because they don't understand nor appreciate rigour and the intrinsic pleasure of the boring problems you describe.

 

[arunma]

I seem to have the opposite experience whereby the physics students seem to struggle with the maths when it gets a little complex. Basically the mathematically able students are better at physics. To compare someone who has done a subject and hasn't about knowledge in the subject is unfair.

Really? Perhaps you could elaborate a bit further. I'm not saying you're wrong, it's just that it's extremely difficult for me to imagine a physics student getting very far without a fairly strong mathematical ability. From my first semester of freshman physics, the subject was mathematically quite intense. There's a lot of algebraic manipulation, trigonometry, plane and analytic geometry, calculus, Taylor series, and vector analysis. Granted, pretty much none of the math I learned after fourth semester calculus was useful to me in physics. But neither myself nor any of my fellow physics students ever had any problems with the mathematics involved in the science. Many of us even took advanced undergraduate math classes involving mathematical rigor (as I said earlier, I took enough to pick up a math degree on the way). I guess what I'm trying to say in short is: a physics student who isn't good at math is going to fail out pretty quickly (=2nd or 3rd semester).

I can't see a physicist going into math because they don't understand nor appreciate rigour and the intrinsic pleasure of the boring problems you describe.

Yes, I do admit that most physics students don't really have an appreciation for the rigor of mathematics. I admit that at some level, it comforts me that all the smarmy mathematical tricks I use in physics do ultimately have a sound, mathematical basis. Mathematics isn't something I'd want to do as a career, because as I said, I find logical constructions to be pretty boring. But I can see how others like yourself might enjoy this sort of thing.

 

[Werg22]

There's a lot of algebraic manipulation, trigonometry, plane and analytic geometry, calculus, Taylor series, and vector analysis.

These fields are very, very trivial to mathematicians. By no means mastery of these make you a strong mathematician. I am not a mathematician myself, but I do know so far. Mathematically talented people tend to struggle more with physics because they often look for deeper understanding than most - but when they understand, they understand better than most.

 

[pivoxa15]

These fields are very, very trivial to mathematicians. By no means mastery of these make you a strong mathematician. I am not a mathematician myself, but I do know so far. Mathematically talented people tend to struggle more with physics because they often look for deeper understanding than most - but when they understand, they understand better than most.

True, i.e Witten, Dirac.

 

[arunma]

These fields are very, very trivial to mathematicians. By no means mastery of these make you a strong mathematician.

Heh, this certainly is true. From my own mathematical experiences, I can say that the difference between my four semesters of calculus, and the rest of my math courses, was like day and night. Nonetheless, the things I mentioned are important prerequisites to being a good mathematician. That might be why I've found that physicists do well at math.

 

[eGuevara]

I'd just like to quote Mr Feynman here:

Physics is to math what sex is to masturbation.

Sorry to spam the thread, I just like quoting Feynman.

 

[pivoxa15]

I'd just like to quote Mr Feynman here:
Sorry to spam the thread, I just like quoting Feynman.

But the thing is Feynman probably never got into deep pure maths. He veiwed maths only as a caculating tool and so in that way I can see why he said what he said.

I can imagine a mathematician (infact Godel) saying the same thing except replace physics with maths but mathematicians probably won't say such 'rough' things.

 

[SeReNiTy]

Sorry to burst your bubble, but a lot of the cutting edge work in various theoretical fields is essentially mathematics. Proving existence for certain PDE's...etc..

 

[Data]

From the perspective of someone who has just completed degree requirements in a math-physics major (I happen to plan to pursue mathematics in graduate school, but I've actually done more research-wise in physics [high energy phenomenology]):

It can be a little bit frustrating to take certain physics courses when you have a stronger background in mathematics. The reason is that physics is necessarily presented in a non-axiomatic, and not-fully-rigorous way.

Certainly, physical models can be constructed axiomatically and dealt with rigorously; However, the objective of teaching physics at the undergraduate level is primarily to develop physical intuition and ways to approach physical systems, not to demonstrate the formal details of models. An accurate description of the goals of (theoretical) physics would be to "guess the universe's axioms." So, while many many successful models in varying contexts are introduced to students, the objective is explicitly not to indoctrinate them into a particular way of thinking, but to encourage intelligent application of different models to describe different systems.

On the other hand, mathematics students are typically accustomed to results presented in full rigor under some system of axioms. Thus, it can be disorienting to them to be presented with systems in which what model to apply is unclear. I've never had a physics class in which the axioms of a given model were laid out in any transparent manner; students are usually expected to reason them by osmosis. Math students often don't like that.

However, when mathematics students are able to adapt themselves to a "physics perspective" on problems and models, the requisite background in analysis of abstracted problems can help immensely.

Physics students are typically very strong at what mathematicians consider to be arithmetic: symbolic manipulation, vector calculus, trigonometry, and the lot. But trying to explain to the average physics student, in a reasonable amount of time, how, say, Clebsch-Gordan coefficients arise, or what a Hilbert space is, is a hopeless proposition (I can count no fewer than five occasions in the past year that I've overheard physics students asking professors to explain to them "what is an inner product?," even after numerous discussions in lectures).

So, a background in pure mathematics can help you out a lot in physics, but only if you are able to adapt yourself into a mindset amenable to doing physics. There are, of course, many many ways in which a background in applied mathematics can help you with physics, but those are typically the things that all physics students are expected to learn (to some degree) anyways.

 

[CPL.Luke]

^agreed

however one thing that I've learned about physics in relation to math, is that they are two entirely different studies in the same language. physicists are essentially the poets who manipulate the language and read all of the grammar books in order to write their poems. While the mathematicians are the grammarians who ponder the structure of the language.physics can never truly be taught through the use of axioms as most of the physics involves an understanding of the fundamentals at play, and then writing an expression for these concepts. Whereas in math you start out with an expression (an axiom, or theorem), and through various manipulations make it apply to something else.

I also noticed this trend in calc based statistics, I found myself using the same sort of intuition to solve the problems rather than basic formulae that you find in various theorems.

however one thing to always remember is that no good poet is ignorant of the language he writes in.

 

[mathwonk]

i think you should go with what you love. The physicists I know are not particularly good at math, and the mathematicians are not particularly good at physics. there are exceptions of course.

True a lot of physicists "know" and use a lot of math, but to a mathematician they do not always seem to understand it. Vice versa the mathematicians do not always seem to grasp the physics that well.

The physicists do come to the mathematicians for help in the mathematical aspects of their work, but the mathematicians also come to the physicists for insight into the physical meaning of the math.

The fact that a lot of physicists come to math guys for help probably reflects their modesty and willingness to ask for help more than their ignorance. This willingness to ask for help is actually a sign of wisdom.

The interaction is a 2 way street with benefits to both parties.

 

[arunma]

From the perspective of someone who has just completed degree requirements in a math-physics major (I happen to plan to pursue mathematics in graduate school, but I've actually done more research-wise in physics [high energy phenomenology]):

Data, after reading your post I must say that I found your comments to be very interesting. As you know I also was a physics and math major, but unlike you, I always considered myself a "physics person" (I'm going to grad school in physics, but I did consider math for a semester or so). Since I always saw things from a physics perspective, I never had trouble with the fact that physicists didn't present theoretical models from an axiomatic perspective. On the contrary, I think it would have troubled me if they did, since I tend to see science as based on intution rather than rigor. Curiously, I didn't have a problem with the axiomatic approach to mathematics, but that was probably because I've always viewed physics and math as entirely separate disciplines. I have to admit though, I tended to take courses that focused more on computation than rigor, so maybe I'm not as good at mathematical proofs as I think I am.

I guess it just goes to show that physicists and mathematicians think very differently. Alas, I think we both know that we wouldn't be able to get along without one another, so it's probably a good thing that we have both types of individuals.

 

[pivoxa15]

While the mathematicians are the grammarians who ponder the structure of the language.

Not always true. In fact most mathematicians (even pure mathematicians) don't work at the foundation level. Most create mathematics just like poets as opposed to pondering only about the axioms.

 

[Data]

Since I always saw things from a physics perspective, I never had trouble with the fact that physicists didn't present theoretical models from an axiomatic perspective. On the contrary, I think it would have troubled me if they did, since I tend to see science as based on intution rather than rigor.Curiously, I didn't have a problem with the axiomatic approach to mathematics, but that was probably because I've always viewed physics and math as entirely separate disciplines.

Indeed. I don't think it would make any sense to present physics axiomatically either, when all we'll ever have are (hopefully, increasingly better) guesses approximating what we think the real "axioms" might be!

I have definitely gotten the impression (from helping other students) that that difference is a big part of the reason why people who have spent years in upper year math courses sometimes have difficulty with even beginning topics in physics, though.

I guess it just goes to show that physicists and mathematicians think very differently. Alas, I think we both know that we wouldn't be able to get along without one another, so it's probably a good thing that we have both types of individuals.

Definitely. Even today, mathematicians would have trouble without the motivations that physics provides (the main reason that the structure of mathematics has developed the way it has is, of course, because the universe happens to be the way that it is!), and physics would have a hard time describing anything without mathematical tools and formalism. The historical development of the two subjects has been interconnected at an absolutely fundamental level, even though the approaches and methods of presentation needed may differ drastically.

 

[Data]

Not always true. In fact most mathematicians (even pure mathematicians) don't work at the foundation level. Most create mathematics just like poets as opposed to pondering only about the axioms.

It might be more appropriate to say that mathematicians work to extend the language, in the hope of giving it yet more depth and power.

 

[arunma]

Oh and incidentally, I must admit that I don't know anything about Clebsch-Gordan coefficients. But I do know about Hilbert space; it's actually a pretty important concept in quantum mechanics. Of course, in the physicists' tradition of mathematical oversimplification, what we call "Hilbert space" is actually just an L² inner product space. Apparently, Hilbert space to a mathematician is more complicated.

 

[CPL.Luke]

eh you are missing a criical definition or any physicist as well, a hilbert space is also complete with respect to some basis, ie any funcion that is in the space has a Fourier decomposition with respect to the basis.

That part of the definition is very imprant for solving pde's, however my favorite simplification is to shift the boundary conditions so tha they go from something like 0 to L rather than -L/2 to L/2 or something like that, as it gets rid of the the cosines.

 

[pivoxa15]

Back to the original question, I think for most people it is harder to learn a discipline like pure maths because we are not naturally adapted to think rigorously but intuition is more to our liking and thinking about the universe is more 'natural' and advantageous from an evolutionary point of view than pure maths. In this way, it is easier to pick up physics then pure maths, should one decide to change careers later on.

 

[JasonRox]

Back to the original question, I think for most people it is harder to learn a discipline like pure maths because we are not naturally adapted to think rigorously but intuition is more to our liking and thinking about the universe is more 'natural' and advantageous from an evolutionary point of view than pure maths. In this way, it is easier to pick up physics then pure maths, should one decide to change careers later on.

Why does everyone think of pure math as some rigorous painful thing?

IT'S NOT!

If you understand it, it also becomes intuitive. It becomes you're environment.

Honestly, physics is no more intuitive than pure math is.

 

[JasonRox]

I seem to have the opposite experience whereby the physics students seem to struggle with the maths when it gets a little complex. Basically the mathematically able students are better at physics. To compare someone who has done a subject and hasn't about knowledge in the subject is unfair.

I can't see a physicist going into math because they don't understand nor appreciate rigour and the intrinsic pleasure of the boring problems you describe.

Man, you generalize wwwwwwwwwwwaaaaaaaaaayyyyyyyyyyyy too much.

Physicists don't understand or appreciate rigour... hmmm... where is the bull**** flag when you need it.

The mathematically able physics student is better at physics... hmmm... we need another bull**** flag here.

I'm going into pure math, and I have no idea where you get these ideas from. I've taken Physics courses too. It's either you don't know what's going on or you're arrogant about math students or something.

 

[JasonRox]

But the thing is Feynman probably never got into deep pure maths. He veiwed maths only as a caculating tool and so in that way I can see why he said what he said.

I can imagine a mathematician (infact Godel) saying the same thing except replace physics with maths but mathematicians probably won't say such 'rough' things.

How did you interpreted the quote? Sounds like Feymann was right if you think about it.

Physics uses mathematics to play around with the world. But mathematics just enjoys itself.

Hence, you use your dick to play with girls (the world), and with masturbation you just enjoy yourself.

Makes complete sense to me. I'd say you nailed the idea spot on.

Who knows what Godel would of that?

 

[naab]

I see math as a tool for physics. Kinda like the pencil for writing.. But I find physics far more fascinating than math.. Don't really think math is "fun" at the same way at all.. Like someone said, I think mathematicians are working on boring problems..

 

[pivoxa15]

Why does everyone think of pure math as some rigorous painful thing?

IT'S NOT!

If you understand it, it also becomes intuitive. It becomes you're environment.

Honestly, physics is no more intuitive than pure math is.

All the difference is in the big 'if' you have there. A lot of time is recquired to understand pure maths. But once you do than things become easier. Like all things, they are hard before they become easy.

Some parts of physics like Newtonian physics is intuitive whereas no branch of pure maths is intuitive to me.

 

[pivoxa15]

Man, you generalize wwwwwwwwwwwaaaaaaaaaayyyyyyyyyyyy too much.

Physicists don't understand or appreciate rigour... hmmm... where is the bull**** flag when you need it.

The mathematically able physics student is better at physics... hmmm... we need another bull**** flag here.

I'm going into pure math, and I have no idea where you get these ideas from. I've taken Physics courses too. It's either you don't know what's going on or you're arrogant about math students or something.

By rigour, I mean mathematical rigour. Physicists are certainly more rigorous than the average Joe.

By physics, I mean theoretical physics and I have good evidence for that.

 

[JasonRox]

whereas no branch of pure maths is intuitive to me.

Right now, but parts of it is. That's what you need to realize.

 

[pivoxa15]

How did you interpreted the quote? Sounds like Feymann was right if you think about it.

Physics uses mathematics to play around with the world. But mathematics just enjoys itself.

Hence, you use your dick to play with girls (the world), and with masturbation you just enjoy yourself.

Makes complete sense to me. I'd say you nailed the idea spot on.

Who knows what Godel would of that?

I think Feynman was also comparing the different levels and types of enjoyment of both activities in that quote.

Godel thought that the 'real' or 'true' world is not this one but a platonic world. To describe playing in this platonic world probably needs a new word.